Question:
Noah loses 76% by selling an article for $878.40. For how much should he sell it to get a profit of 75%?
Correct Answer
6405
Solution And Explanation
Strategy to solve the question
Step (1) Calculate the cost price at given loss percent and the sale price.
Step (2) After gettting the cost price find the sale price at given profit percent.
Solution
Method (1) Formula Method
Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given
Given, the sale price (SP) = $878.4
And, the loss = 76%
Then, the Sale Price (SP) to earn a profit of 75% = ?
Formula to find the cost price when the sale price and loss percent are known
Cost Price (CP) = 100/100 – gain% × SP
Thus, the Cost Price (CP)
= 100/100 – 76 × 878.4
= 100/24 × 878.4
= 100 × 878.4/24
= 87840/24 = 3660
Thus, the Cost Price (CP) = $3660
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $3660
And, profit = 75%
Thus Sale Price (SP) = ?
Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known
Sale Price (SP) = 100 + gain%/100 × Cost Price (CP)
Thus, the Sale Price (SP)
= 100 + 75/100 × 3660
= 175/100 × 3660
= 175 × 3660/100
= 640500/100 = 6405
Thus, Sale Price (SP) at a profit of 75% = $6405 Answer
Method (2) Algebraic Method
Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given
Given, the sale price (SP) = $878.4
And, the loss = 76%
Then, the Sale Price (SP) to earn a profit of 75% = ?
Let the Cost Price (CP) = m
Here given loss = 76%
Calculation of loss
loss is calculated on cost price (CP)
Formula to find the loss = loss% of CP
Thus, loss on the cost price of m
= 76% of m
= 76% × m
= 76/100 × m
⇒ loss = 76 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 878.4 = m – 76 m/100
⇒ 878.4 = 100 m – 76 m/100
⇒ 878.4 = 24 m/100
After cross multiplication, we get
878.4 × 100 = 24 m
⇒ 24 m = 878.4 × 100
⇒ m = 878.4 × 100/24
⇒ m = 87840/24 = 3660
⇒ m = 3660
Thus, the Cost Price (CP) = $3660
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 3660
And, the profit = 75%
Thus, Sale Price (SP)
= Cost Price (CP) + 75% of Cost Price (CP)
= 3660 + 75/100 × 3660
= 3660 + 75 × 3660/100
= 3660 + 274500/100
= 3660 + 2745 = 6405
Thus, Sale Price (SP) at a profit of 75% = $6405 Answer
Method (3) Unitary Method
Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given
Given, the sale price (SP) = $878.4
And, the loss = 76%
Then, the Sale Price (SP) to earn a profit of 75% = ?
Let, CP = 100
75% profit = 75% of CP
= 75% of 100 = 75
Thus, Sale Price to earn a profit of 75% = CP + 75
= 100 + 75 = 175
⇒ Sale Price to earn a profit of 75% = 175
76% loss = 76% of CP
= 76% of 100 = 76
Thus, Sale Price at a loss of 76% = CP – Loss
= 100 – 76 = 24
⇒ Sale Price at a loss of 76% = 24
∵ If the Sale Price is 24, then to earn a profit of 75% the Sale Price should be = 175
∴ If the Sale Price is 1, then to earn a profit of 75% the Sale Price should be
= 175/24
∴ If the Sale Price is 878.4, then to earn a profit of 75% the Sale Price should be
= 175/24 × 878.4
= 175 × 878.4/24
= 153720/24 = 6405
Thus, Sale Price to get a profit of 75% = $6405 Answer
Method (4) Shortcut Method
Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given
Given, the sale price (SP) = $878.4
And, the loss = 76%
Then, the Sale Price (SP) to earn a profit of 75% = ?
Here, the Sale Price at a loss of 76 = $878.4
This means 24% of the Cost Price (CP) = 878.4
Therefore, 1% of the Cost Price (CP) = 878.4/24
Therefore, 100% of the Cost Price (CP)
= 878.4/24 × 100 = 3660
Thus, the Cost Price (CP) = $3660
Now, we need to find the Sale Price at a profit of 75%
Thus, Sale Price at a profit of 75%
= 175% of the Cost Price (CP)
= 175% of 3660
= 175/100 × 3660 = 6405
Thus, the Cost Price at a profit of 75% = $6405 Answer
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